Wind Tunnel Tests and Wake Effects of Pitch and Load ... Schottler ForWind, University of Oldenburg Wind Tunnel Tests and Wake Effects of Pitch and Load Controlled Model Wind Turbines

Jannik SchottlerForWind, University of Oldenburg

Wind Tunnel Tests and Wake Effects of Pitch and Load Controlled Model Wind Turbines

ForWind, Center for Wind Energy Research, University of Oldenburg

Jannik Schottler, A. Hölling, J. Peinke, M. Hölling

[email protected]

mailto:[email protected]

mailto:[email protected]

Jannik Schottler / ForWind, University of Oldenburg 2

Motivationwind farms: interaction of turbines inevitable !

‣ power losses due to wake effects‣ increased loads

understanding of interactions necessary

[Barthelmie et.al. 2010]

[Crespo et.al. 1999]






inflow/turbine







inflow/turbine turbine/wake







inflow/turbine turbine/wake wake/turbine



Methods

Field measurements:expensive, changing boundary conditions, limited availability


Methods


CFD:often model-based,

(computational) costs, validation?


Methods


Experiments:inexpensive, tunable boundary conditions,

upscaling?




Methods


Experiments:inexpensive, tunable boundary conditions,

upscaling?



validation


Wakes of Wind Turbines

behind the rotor...



behind the rotor...

Decreased wind speed

‣power losses

Increased turbulence intensity

‣higher loads


wind direction


behind the rotor...


‣power losses


‣higher loads


wind direction


behind the rotor...


‣power losses


‣higher loads


v

y

wind direction


behind the rotor...


‣power losses


‣higher loads


v

y

wind direction

Wind Energ. 2010; 13:559–572 © 2009 John Wiley & Sons, Ltd.DOI: 10.1002/we

560

Wake defl ection of a wind turbine in yaw Á. Jiménez, A. Crespo and E. Migoya

tensor proposed by Gómez-Elvira et al.7 In all these previ-ous methods, the Reynolds average over all turbulence scales is imposed. Instead, LES will reproduce the unsteady oscillations of the fl ow characteristics over all scales larger than the grid size; consequently, a greater detail of the turbulence characteristics is expected to be obtained. In Jiménez et al.,4 a LES computation of the wake was per-formed immersing an actuator disk-modelled turbine in an environment with turbulence properties similar to the ones of the atmosphere. A similar technique is used by other authors like Masson,8 Kasmi and Mason,9 etc. Together with the actuator disk approach, it must be highlighted the actuator line representation given by Sørensen and Shen,10 recently used by Troldborg et al.11 to carry out a detailed LES analysis of a wind turbine wake under uniform infl ow conditions.

Jiménez et al.4 gave a comparison of LES results with experimental data obtained by Cleijne12 from the Sex-bierum wind farm and with analytical correlations pre-viously proposed by Crespo and Hernández13 and Gomez-Elvira et al.7 In the present work, application of the same technique to study the steady wake defl ection of a wind turbine in yaw is made.

Control of turbine parameters in wind farms has been suggested as a method to increase the power production of the whole wind farm and to reduce fatigue loads due to the high level of turbulence in wakes. Corten and Shaak14 proposed a strategy based on decreasing the axial induc-tion factor (through pitch angle control) at the upwind side of the wind farm in order to get a higher wind speed in the wake and, consequently, a larger amount of available kinetic energy for the turbines under the lee side. The research presented in this paper can give an illustration of future possibilities to plan an active control to minimize the interference effects in wind farms, now based on the yaw of wind turbines.

When a wind turbine works in yaw, the wake intensity and the power production of the turbine become slightly smaller and a defl ection of the wake is induced. A suffi -ciently good understanding of this effect would allow an active control of the yaw angle of upstream turbines to steer the wake away from downstream machines, as illus-trated in Figure 1, reducing its effect on them and giving as consequence an optimization of the power output from the wind farm as a whole. Also a reduction of fatigue loads on downstream turbines due to a lower increase of turbu-lence intensity in wakes is achieved. However, possibly this also increases the fatigue in the fi rst turbine, since yawing itself may cause fatigue; accordingly, it should be quantifi ed if the net result is favourable.

The gross wake defl ection in yaw was shown by Clayton and Filby15 who performed hot-wired measurements in the wake of a wind turbine at a number of downstream posi-tions. Particle image velocimetry (PIV) technique was used by Grant et al.16 and Grant and Parkin17 enabling a detailed understanding of vortex formation and expansion phenomena in the near wake, both in yawed and non-yawed conditions, and giving information about the initial

skew angle of the wake of a yawed turbine. Concerning the interaction between machines, it is more relevant the experimental study done by Parkin et al.18 They obtained PIV images in the wake of a two bladed HAWT at dis-tances from one to fi ve diameters downstream, for differ-ent values of the yaw angle. Their PIV experiments were carried out with a two-bladed model wind turbine in a low turbulence wind tunnel at Kungliga Tekniska Högskolan (KTH), Sweden. Model turbines may not behave as full-sized ones and, consequently, it would be of interest to rely also on experimental measurements obtained on fi eld. Unfortunately, data about full-sized turbines operating in yaw conditions are scarce.

In this work, a preliminary analysis of wakes of wind turbines in yaw is presented. The wake defl ection and trajectories are studied and compared to a simple analytical model and with experimental results.

2. LES MODEL WITH SIMPLIFIED BOUNDARY CONDITIONS

Only a direct simulation of turbulence would be able to give us the full knowledge of the turbulence characteristics in the wake. In industrial or environmental applications, where Reynolds numbers are usually very high, direct-numerical simulations (DNS) of turbulence are generally impossible because the very wide range that exists between the largest and the smallest turbulent scales cannot be explicitly simulated, even in the most powerful computers. Furthermore, DNS is not feasible near rough boundaries

Figure 1. Recreation of the wake defl ection due to a wind turbine in yaw.

Jiménez et al. 2010



v

y

wind direction

Wind Energ. 2010; 13:559–572 © 2009 John Wiley & Sons, Ltd.DOI: 10.1002/we

560

Wake defl ection of a wind turbine in yaw Á. Jiménez, A. Crespo and E. Migoya

tensor proposed by Gómez-Elvira et al.7 In all these previ-ous methods, the Reynolds average over all turbulence scales is imposed. Instead, LES will reproduce the unsteady oscillations of the fl ow characteristics over all scales larger than the grid size; consequently, a greater detail of the turbulence characteristics is expected to be obtained. In Jiménez et al.,4 a LES computation of the wake was per-formed immersing an actuator disk-modelled turbine in an environment with turbulence properties similar to the ones of the atmosphere. A similar technique is used by other authors like Masson,8 Kasmi and Mason,9 etc. Together with the actuator disk approach, it must be highlighted the actuator line representation given by Sørensen and Shen,10 recently used by Troldborg et al.11 to carry out a detailed LES analysis of a wind turbine wake under uniform infl ow conditions.

Jiménez et al.4 gave a comparison of LES results with experimental data obtained by Cleijne12 from the Sex-bierum wind farm and with analytical correlations pre-viously proposed by Crespo and Hernández13 and Gomez-Elvira et al.7 In the present work, application of the same technique to study the steady wake defl ection of a wind turbine in yaw is made.

Control of turbine parameters in wind farms has been suggested as a method to increase the power production of the whole wind farm and to reduce fatigue loads due to the high level of turbulence in wakes. Corten and Shaak14 proposed a strategy based on decreasing the axial induc-tion factor (through pitch angle control) at the upwind side of the wind farm in order to get a higher wind speed in the wake and, consequently, a larger amount of available kinetic energy for the turbines under the lee side. The research presented in this paper can give an illustration of future possibilities to plan an active control to minimize the interference effects in wind farms, now based on the yaw of wind turbines.

When a wind turbine works in yaw, the wake intensity and the power production of the turbine become slightly smaller and a defl ection of the wake is induced. A suffi -ciently good understanding of this effect would allow an active control of the yaw angle of upstream turbines to steer the wake away from downstream machines, as illus-trated in Figure 1, reducing its effect on them and giving as consequence an optimization of the power output from the wind farm as a whole. Also a reduction of fatigue loads on downstream turbines due to a lower increase of turbu-lence intensity in wakes is achieved. However, possibly this also increases the fatigue in the fi rst turbine, since yawing itself may cause fatigue; accordingly, it should be quantifi ed if the net result is favourable.

The gross wake defl ection in yaw was shown by Clayton and Filby15 who performed hot-wired measurements in the wake of a wind turbine at a number of downstream posi-tions. Particle image velocimetry (PIV) technique was used by Grant et al.16 and Grant and Parkin17 enabling a detailed understanding of vortex formation and expansion phenomena in the near wake, both in yawed and non-yawed conditions, and giving information about the initial

skew angle of the wake of a yawed turbine. Concerning the interaction between machines, it is more relevant the experimental study done by Parkin et al.18 They obtained PIV images in the wake of a two bladed HAWT at dis-tances from one to fi ve diameters downstream, for differ-ent values of the yaw angle. Their PIV experiments were carried out with a two-bladed model wind turbine in a low turbulence wind tunnel at Kungliga Tekniska Högskolan (KTH), Sweden. Model turbines may not behave as full-sized ones and, consequently, it would be of interest to rely also on experimental measurements obtained on fi eld. Unfortunately, data about full-sized turbines operating in yaw conditions are scarce.

In this work, a preliminary analysis of wakes of wind turbines in yaw is presented. The wake defl ection and trajectories are studied and compared to a simple analytical model and with experimental results.

2. LES MODEL WITH SIMPLIFIED BOUNDARY CONDITIONS

Only a direct simulation of turbulence would be able to give us the full knowledge of the turbulence characteristics in the wake. In industrial or environmental applications, where Reynolds numbers are usually very high, direct-numerical simulations (DNS) of turbulence are generally impossible because the very wide range that exists between the largest and the smallest turbulent scales cannot be explicitly simulated, even in the most powerful computers. Furthermore, DNS is not feasible near rough boundaries

Figure 1. Recreation of the wake defl ection due to a wind turbine in yaw.

Jiménez et al. 2010


Jannik Schottler / ForWind, University of Oldenburg

D=58cm

variable pitch, variable speed

automated control

measured variables:

vacuum-casted blades (SD7003)

data acquisition/control in RealTime

6

P,!,�, T

Model Wind Turbines


collective pitch

closed-loop

7

generator

stepper motor

main shaftslider

�� 30�

Pitching Mechanism


collective pitch

closed-loop

7

generator

stepper motor

main shaftslider

�� 30�

Pitching Mechanism


inactive control

0 20 40 60 80 1000

5

10

P[W

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

0 20 40 60 80 1000

20

40

60

cP[%

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

Partial Load Control


inactive control

0 20 40 60 80 1000

5

10

P[W

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

0 20 40 60 80 1000

20

40

60

cP[%

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

cP / P⌫�3



inactive control

0 20 40 60 80 1000

5

10

P[W

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

0 20 40 60 80 1000

20

40

60

cP[%

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

active control

0 20 40 60 80 1000

5

10

P[W

]

t [s]0 20 40 60 80 100

4

5

6

ν[m

s−1]

0 20 40 60 80 1000

20

40

60

cP[%

]t [s]

0 20 40 60 80 100

4

5

6

ν[m

s−1]

cP / P⌫�3



x

Prandtl-Sonden

Wind

A1 A2

tube

T1 T2

�

Tandem Setup


T2: independent partial load control - maximizing cp

T1: systematic variation of

9

x

Prandtl-Sonden

Wind

A1 A2

tube

T1 T2

�, � �

Tandem Setup


T2: independent partial load control - maximizing cp

T1: systematic variation of

9

x

Prandtl-Sonden

Wind

A1 A2

tube

T1 T2

�, � �

Tandem Setup


x/D=3

asymmetric�P,min ⇡ �6�

P2

γ1 [deg]-40 -20 0 20 40

P/Pmax[−

]

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1γ

min → γ

max

γmax

→ γmin

Results


x/D=3

asymmetric�P,min ⇡ �6�

P2

γ1 [deg]-40 -20 0 20 40

P/Pmax[−

]

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1γ

min → γ

max

γmax

→ γmin

Ptot

asymmetric

+6%!

�P,max

⇡ 18�

γ1 [deg]-40 -20 0 20 40

P/Pmax[−

]

0.75

0.8

0.85

0.9

0.95

1

γmin

→ γmax

γmax

→ γmin

Results


Ptot

P2

SOFWA Simulation

2 NREL 5MW turbines

x/D = 7

u=8m/s, TI=6%

γ1 [deg]-40 -20 0 20 40

P/Pmax[−

]

0.75

0.8

0.85

0.9

0.95

1

γmin

→ γmax

γmax

→ γmin

Gebraad et. al.

γ1 [deg]-40 -20 0 20 40

P/Pmax[−

]

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1γ

min → γ

max

γmax

→ γmin

Gebraad et. al.

Results


two ‘variable speed, variable pitch’ model wind turbines

tested partial load control

12

Tandem Setup

Summary


two ‘variable speed, variable pitch’ model wind turbines

tested partial load control

12

improved power output for yaw misalignment in tandem-configuration

‣ +6% for x/D=3 at 18° yaw misalignment of T1

in good agreement with simulations!

Tandem Setup

Summary


Outlook


turbulent inflow

active grid

Outlook


thrust measurementsturbulent inflow

active grid

Outlook


inflow/turbine interaction


active grid

Outlook

detailed wake characterization(hot wires, PIV)




active grid

Outlook




turbine/wake interaction


active grid

‣ yaw

‣ pitch

‣ TSR

Outlook




turbine/wake interaction wake/turbine

interaction


active grid

‣ yaw

‣ pitch

‣ TSR

Outlook


,custom‘ turbulence

Active Grid



Active Grid



LiDAR measurements by Risø, DTU

Experiments: ,Smart Blades‘ Project, Nico Reinke, André Fuchs, Tim Homeyer. ForWind, University of Oldenburg

t / s

0 10 20 30 40 50 60U

/ m

/s5

6

7

8

9

10

11

12

13

14

15

Hot wire

LiDAR

Active Grid


Acknowledgement

Parts of this work was funded by the

Thank you for your attention!


Acknowledgement

Parts of this work was funded by the

Thank you for your attention!


raw data, all Ust-values

−50

510

15

0.8

1

1.2

0

10

20

30

40

β [deg]Uwk [V ]

cP[%

]

Uwt [V ]


cP,max

⇡ 40%

raw data, all Ust-values max cp, interpolation

−50

510

15

0.8

1

1.2

0

10

20

30

40

β [deg]Uwk [V ]

cP[%

]

Uwt [V ]

05

1015

0.8

1

1.2

0

10

20

30

40

β [deg]Uwk [V ]

cP[%

]

cP[%

]

0

5

10

15

20

25

30

35

40

45

Uwt [V ]


USt of the maximal cP foreach wind speed

3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data



partial load control!

3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data




measuring v

moving av.0,5s

USt / ⌫

3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data




measuring v

moving av.0,5s

USt / ⌫

3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data

moving av.2s

wind tunnelshut down for!2s > 1500rpm

measuring !


�

opt

:= 0� ⇡ const.

cpmax for different wind speeds and pitch angles

−5 0 5 10 150

5

10

15

20

25

30

35

40

β [deg]

cP[%

]

Uwk [V ] = 0.8Uwk [V ] = 0.9Uwk [V ] = 1Uwk [V ] = 1.1Uwk [V ] = 1.2Uwk [V ] = 1.3Uwk [V ] = 1.4


�

opt

:= 0� ⇡ const.

cpmax for different wind speeds and pitch angles

−5 0 5 10 150

5

10

15

20

25

30

35

40

β [deg]

cP[%

]

Uwk [V ] = 0.8Uwk [V ] = 0.9Uwk [V ] = 1Uwk [V ] = 1.1Uwk [V ] = 1.2Uwk [V ] = 1.3Uwk [V ] = 1.4

cpmax increases with wind speed

due to (mechanical) friction

2 3 4 5 6 720

25

30

35

40

45

cP,m

ax[%

]v [m/s]

lin. Fit

Data


Electrical Load Variation


3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data



⌫ = const.

� = const.

2 2.05 2.1 2.15 2.2 2.25600

800

1000

1200

USt [V ]

ω[r

pm

]

2 2.05 2.1 2.15 2.2 2.250

1

2

3

4

USt [V ]

P[W

]

Electrical Load Variation


3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

ν [m/s]

USt[V

]

β = βopt = 0◦

Fit

Data



exemplary: x/D=4

−5 0 5 10 150

0.2

0.4

0.6

0.8

1

β [deg]

P/Pges,m

ax[-]

A1A2A1+A2


change in pitch influences P2

however: no gain in Ptot !

holds for x/D={3, 5, 6}

exemplary: x/D=4

�P1,opt = �Ptot,opt

−5 0 5 10 150

0.2

0.4

0.6

0.8

1

β [deg]

P/Pges,m

ax[-]

A1A2A1+A2


0 0.5 10

0.5

1

t / Tref [−]

u / <

u> [−

] &

σ/5

[m/s

]

u gridσ/5 gridu ref.σ/5 ref.


0 0.2 0.4 0.6 0.8 1

0.4

0.5

0.6

0.7

0.8

0.9

1

PA1/PA1,max [-]

Pges/Pges,m

ax[-]

x/D=3x/D=4x/D=5x/D=6


0 0.2 0.4 0.6 0.8 1

0.4

0.5

0.6

0.7

0.8

0.9

1

PA1/PA1,max [-]

Pges/Pges,m

ax[-]



0 0.2 0.4 0.6 0.8 1

0.4

0.5

0.6

0.7

0.8

0.9

1

PA1/PA1,max [-]

Pges/Pges,m

ax[-]



0 0.2 0.4 0.6 0.8 1

0.4

0.5

0.6

0.7

0.8

0.9

1

PA1/PA1,max [-]

Pges/Pges,m

ax[-]


Ptot,max and P1,max coincide

no gain in power by changing

to �1 �1 6= �1,opt


partial load control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

inactive control



0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

inactive control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

active control



inactive control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]



inactive control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

active control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]t [s]

0 50 100 150

4

5

6

ν[m

s−1]



inactive control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

active control

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]t [s]

0 50 100 150

4

5

6

ν[m

s−1]

phase shift


0 5 10 15 200.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

y/ymax

x/π

sin(x)sin(x+ φ)sin(x+φ)sin3(x)

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]


0 5 10 15 200.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

y/ymax

x/π

sin(x)sin(x+ φ)sin(x+φ)sin3(x)

0 50 100 1500

5

10

P[W

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

0 50 100 1500

20

40

60

cP[%

]

t [s]0 50 100 150

4

5

6

ν[m

s−1]

cP / P⌫�3


generator

stepper motor

main shaft slider


generator

stepper motor

main shaft slider


collective pitch

“closed-loop”

26

generator

stepper motor

main shaft slider

�� 30�


collective pitch

“closed-loop”

26

generator

stepper motor

main shaft slider

�� 30�

90°βy

xLaserdiode

Flügelhalterung

Gondel

blade mounting

laser diode

gondola


collective pitch

“closed-loop”

26

generator

stepper motor

main shaft slider

�� 30�

0 50 100 150 200 2500

5

10

15

20

25

steps [-]

Pitchwinkel[deg]

set1set2set3set4set5fit

�[deg]

90°βy

xLaserdiode

Flügelhalterung

Gondel

blade mounting

laser diode

gondola


x

y

z

near wake far wakex

turbulente Scherschicht In Näherung:

- gaußförming- axensymmetrisch

v


Dw

Wind

x

⇤

0, 8m

Düse⌫lab = 0ms�1

⌫1

⌫wake < ⌫1

wind tunnel: open test section - free stream

outlet


Dw

Wind

x

⇤

0, 8m


⌫1

⌫wake < ⌫1


Dw = D + 2kx⇤ Jensen 1983:

‣ x⇤/D ⇡ 4, 7

outlet


Dw

Wind

x

⇤

0, 8m


⌫1

⌫wake < ⌫1


Dw = D + 2kx⇤ Jensen 1983:

‣ x⇤/D ⇡ 4, 7

wake reaches edge of free stream!

yaw misalignment intensifies the effect

outlet


wake expansion II wind tunnel: open test section - free stream

Dw

wind0, 8m

outlet⌫lab = 0ms�1

⌫1

⌫wake < ⌫1

x

⇤


wake expansion II wind tunnel: open test section - free stream

Dw

wind0, 8m

outlet⌫lab = 0ms�1

⌫1

⌫wake < ⌫1

x

⇤

turbulent conditions at T2 for large x


�

Aeff = A · cos(�)

Aeff = A

Wind

Wind


�


Aeff = A

Wind

Wind

cos(�) =1X

n=0

(�1)

n �2n

(2n)!= 1� �2

2!

+

�4

4!

� �6

6!

± · · ·

cos(�) ⇡ 1� �2

2!

.


�


Aeff = A

Wind

Wind

cos(�) =1X

n=0

(�1)

n �2n

(2n)!= 1� �2

2!

+

�4

4!

� �6

6!

± · · ·

cos(�) ⇡ 1� �2

2!

.

−60 −40 −20 0 20 40 600.4

0.5

0.6

0.7

0.8

0.9

1

γ [deg]

Amplitude

cos(γ)c1γ

2 + c2


�1 = ��2

~⌫ind1(✓) = ~⌫ind2(✓ + 180�)

uniform flow non-uniform flow

~⌫res = ~⌫ind � ~⌦⇥ ~r + ⌫1

~⌫res1(✓) = ~⌫res2(✓ + 180 �)

de Haans 2011

~⌫res1(✓) 6= ~⌫res2(✓ + 180 �)

~⌫1(✓) 6= ~⌫1(✓ + 180 �)

cT,1 6= cT,2cT,1 = cT,2


T1 in yaw

−40 −20 0 20 400.4

0.5

0.6

0.7

0.8

0.9

1

γA1 [deg]

P/Pmax[−

]

x/D=3

x/D=4

x/D=5

x/D=6

Gebraad et.al.

Wind Tunnel Tests and Wake Effects of Pitch and Load ... Schottler ForWind, University of Oldenburg Wind Tunnel Tests and Wake Effects of Pitch and Load Controlled Model Wind Turbines

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